

Figure REF  summarizes the proximal algorithms
derived from (REF ).
When \(h=0\) , algorithm (REF ) reduces to PDHG
applied to the dual of (REF ) (with \(h=0\) ),
which is shown to be equivalent to linearized ADMM [1]}, [2]}
(also called Split Inexact Uzawa in [3]}).
Setting \(g=0\)  in (REF ) yields the proximal gradient algorithm.
When \(f=0\) , we obtain a new algorithm:
\(z^{(k+1)} &= \mathrm {prox}_{\sigma g^\ast } (z^{(k)}+\sigma Ax^{(k)}) \\x^{(k+1)} &= x^{(k)}-\tau (A^T(2z^{(k+1)}-z^{(k)})+\nabla h(x^{(k)})).\) 
